Receiving apparatus and method for electronic noise compensation in phase modulated optical transmission

ABSTRACT

A receiving apparatus and method for processing a differential phase shift keying signal carrying a plurality of symbols are disclosed to provide for improved compensation of linear and non-linear noise in phase modulated optical transmission. The receiving apparatus comprises an input unit for receiving electrical signals derived from an optical signal and a calculation unit for calculating a current value of a decision variable. The current value is indicative of a differential phase shift in the optical signal between a currently received symbol and a previously received symbol as a function of the optical signal power of the optical signal for the currently received symbol and at least one previous value of the decision variable. The receiving apparatus also comprises a decision unit for determining the differential phase shift from the current value of the decision variable obtained from the calculation unit to obtain the currently received symbol.

TECHNICAL FIELD

The present invention relates to a receiving apparatus and method forprocessing a differential phase shift keying signal carrying a pluralityof symbols.

BACKGROUND

Phase shift keying (PSK) is a modulation scheme for transmitting data bychanging or modulating, the phase of a reference signal, constituting acarrier wave. PSK uses different phases, commonly two or four, whereinfor each a unique pattern of binary bits is assigned. Each bit patternforms a symbol that is represented by the particular phase. Indemodulation, the phase of the received signal is determined and ismapped back to the symbol it represents to recover the original data.Thereby, the phase of the received signal is compared to the unshiftedreference signal. This process is called coherent detection.

Alternatively, which is more widely used, non-coherent detection may beused. Here, instead of setting the phase of the wave, data may bemodulated onto the carrier wave by changing the phase by a specificamount with respect to a previous phase shift. Therefore, a signal thathas been differentially encoded to comprise information may simply bedemodulated by detecting the phase between two successively receivedsymbols, i.e. the changes in the phase of the received signal ratherthan the phase itself are determined. Since this scheme depends on thedifference between successive phases, it is termed differential phaseshift keying (DPSK).

In non-coherent demodulation or detection, demodulators may thus beused, which operate without knowledge of the absolute value of the phaseof the incoming signal reducing the complexity of the system butincreasing the probability of error. In detail, once a previous symbolis corrupted, i.e. the previous differential phase shift was distortede.g. by noise; the error will propagate to the next symbol, since theprevious phase is used for the determination of the next symbol.Therefore, it is important to reduce noise in the system to obtaincorrect symbols.

The carrier wave is usually realized by optical transmission. Here,phase modulated optical transmission may be corrupted by linear andnon-linear phase noise which is accumulated along an opticaltransmission system.

Linear phase noise is caused, for example, by phase variations resultingfrom added amplified spontaneous emission (ASE) noise of each opticalamplifier in a fiber-optic transmission system.

Non-linear phase noise is caused by a non-linear mixing of a signal withthe optical amplifier noise owed to the non-linear refractive index ofthe transmission fibers, known as Kerr effect. It is often referred toas Gordon-Mollenauer noise.

A convenient way to represent PSK schemes is on a constellation diagramshowing constellation points in a complex plane (Argand plane) where thereal and imaginary axes are termed the in-phase and quadrature axesintersecting each other perpendicularly. The constellation pointsrelated to symbols are usually positioned with uniform angular spacingaround a circle. For example, in quadrature phase shift keying (QPSK),which uses four different phases, four constellation points aredistributed along the circle, preferably so that in each quadrant of thediagram there is one constellation point. In this example, two bits persymbol represented by a constellation point can be encoded.

Both the linear and non-linear phase noise spread signal constellationpoints, albeit in a different way, and degrade the transmissionperformance of optical differential phase shift keying (DPSK) anddifferential quadrature phase shift keying (DQPSK) signals. In otherwords, the phase relation between successive symbols changes with phasenoise, increasing the error rate.

For simplicity, a self-homodyne scheme is often used to demodulateoptical phase modulated signals as it eliminates the need for a localphase reference at the receiver, as explained above with respect toDPSK. Such a scheme aggravates, however, the noise impact because asevere corruption of the previous symbol is likely to cause a corruptionof the current symbol also, since in this scheme the phase correspondingto the previous symbol constitutes the reference. In the linear regime,self-homodyne reception yields a performance penalty of ˜0.5 dB for DPSKand ˜2 dB for DQPSK signals when compared to ideal homodyne detection,as discussed in patent application, EP 1 694 017 A1.

For mitigation of the linear phase noise and specifically the base linepenalty of self-homodyne detection, receivers with electroniccompensators based on multi-symbol phase estimation (MSPE) or multiplesymbol differential detection (MSDD) have been proposed, for example byH. Leib in “Data-aided noncoherent demodulation of DPSK” IEEE Trans.Commun., Vol. 43, 1995 and U.S. Pat. No. 5,017,883, respectively.

An adaptation of MSPE to optical phase modulated systems withself-homodyne detection can be found, for example, in the papers by X.Liu, “Generalized data-aided multi-symbol phase estimation for improvingreceiver sensitivity in direct-detection optical m-ary DPSK”, OpticsExpress, Vol. 15, No. 6, 2007 and “Receiver sensitivity improvement inoptical DQPSK and DQPSK/ASK through data-aided multisymbol phaseestimation”, Proc. ECOC'06, paper We2.5.6., 2006.

Existing solutions for optical DPSK and DQPSK reception based on MSPEcommonly assume that the signal envelope is constant or only slowlyvarying at the sampling time of the decision device. Whilst this may betrue for ideal systems, e.g. a mismatch from the ideal group velocitydispersion at the receiver and non-linear signal interactions on thetransmission link can cause intersymbol interference (ISI) anddeteriorate the result of the MSPE/MSDD detection process. A modifiedscheme (here referred to as MSPE-E) takes changes in the signal envelopeinto account. With moderate additional effort in the electronic domain,this scheme can also be used to detect combined optical DQPSK/amplitudeshift keying (ASK) (see the above referenced papers by X. Liu) orquadrature amplitude modulated (QAM) signals.

Non-linear phase noise is mostly dependent on the instantaneousintensity of the optical signal. It can be mitigated by reverting thenon-linear phase shift which fluctuations in the light intensity causeon the transmission link (non-linear phase noise compensation, NLPC).

However, existing solutions are expensive and tailored for achievingperformance improvements either in the linear regime or in thenon-linear regime only, using optical or electronic solutions.

SUMMARY

Therefore, the present invention aims at providing a simple andinexpensive way for compensating for linear and non-linear noise inphase modulated optical transmission.

This object is achieved by a receiving apparatus having the features ofindependent claim 1 and by a receiving method having the features ofindependent claim 16.

According to one embodiment, there is provided a receiving apparatus forprocessing a differential phase shift keying signal carrying a pluralityof symbols. The receiving apparatus comprises an input unit forreceiving electrical signals derived from an optical signal afterself-homodyne reception and a calculation unit for calculating a currentvalue of a decision variable. The current value of the decision variableis indicative of a differential phase shift in the optical signalbetween a currently received symbol and a previously received symbol andis calculated as a function of at least one of the electrical signalsrepresenting the optical signal power of the optical signal for thecurrently received symbol and at least one previous value of thedecision variable to correct for phase noise. The receiving apparatusalso comprises a decision unit for determining the differential phaseshift from the current value of the decision variable obtained from thecalculation unit to obtain the currently received symbol.

A receiving apparatus within the meaning of the present application andclaims is any apparatus that provides for receiving optical orelectrical signals and is capable to further process the signalselectronically to obtain a current value of the decision variable forreliably extracting the differential phase shift in an optical system. Adifferential phase shift is the difference in phase between differentparts of the optical signal that have been received at different times,wherein these parts may correspond to different symbols. In a simplecase, a decision may be reached by comparing the value of the decisionvariable to a threshold, but also cases are feasible where the decisioncomprises more than two states. The expression “decision variable” isalso used in the art and denotes a variable useful for accuratelyobtaining the differential phase shift by taking into account distortionin phase due to phase noise.

Accordingly, calculating the current value of the decision variable bytaking into account the optical signal power of the optical signal forthe currently received symbol and at least one previous value of thedecision variable enables to simultaneously compensate for both linearand non-linear phase noise accumulated along a transmission link,including the loss due to interferometric detection. This scheme allowsindependent optimization of respective adaptation parameters andachieves substantial performance improvements over the prior art,especially in the non-linear transmission regime.

Since the compensation is performed electronically, the receivingapparatus can be used with standard optical equipment, thus obtainingimproved results at negligible additional costs. Additionally, thereceiving apparatus may be used together with the same electro-opticalarrangements as used for DPSK/DQPSK/DQPSK-ASK signals.

According to an advantageous example, the calculation unit is configuredto base the calculation of the decision variable on at least one of adifference between optical signal powers of the optical signal for thecurrently received symbol and for a previously received symbol, anoptical signal power of the previously received symbol, a weightingfactor, an adaptation factor determining the strength of non-linearphase noise compensation, a symbol period of the optical signal, and adifferential phase shift between the previously received symbol and asymbol received before the previously received symbol. Accordingly,different parameters may be given to the calculation unit to enhance thecalculation of the decision variable. In particular, the parameters areconsidered in electronic processing simplifying the requirements on thecalculation unit and keeping the costs low.

According to another advantageous example, the calculation unit isconfigured to calculate the current value of the decision variable usinga multiplication factor representable as a complex exponential functionhaving the adaptation factor and the difference between the opticalsignal powers of the optical signal for the currently received symboland for the previously received symbol in the exponent. Accordingly, avalue of a decision variable may be calculated that is useful to obtainthe differential phase shift more accurately by taking into accountnon-linear phase noise introduced between the current symbol and theprevious symbol.

According to another advantageous example, the calculation unit isconfigured to perform the calculation of the current value of decisionvariable on a basis of an equation dependent on a complex envelope ofthe differentially decoded signal, the adaptation factor, the differencebetween optical signal powers of the optical signal for the currentlyreceived symbol and for the previously received symbol, the weightingfactor, the previous value of the decision variable, the optical signalpower of the previously received symbol and the differential phase shiftbetween the previously received symbol and a symbol received before thepreviously received symbol. Accordingly, a value of the decisionvariable may be calculated electronically that is useful to obtain thedifferential phase shift more accurately.

According to another advantageous example, the electrical signalscorrespond to the optical signal power of the optical signal for thecurrently received symbol and at least one of the real part of thecomplex envelope of the differentially decoded signal and the imaginarypart of the complex envelope of the differentially decoded signal.Accordingly, two electrical signals are sufficient to calculate anaccurate value of the decision variable, e.g. for binary phase shiftkeying (BPSK).

According to another advantageous example, the receiving apparatusfurther comprises a first delay unit for providing the electrical signalcorresponding to the optical signal power of the previously receivedsymbol to the calculation unit to calculate the current value of thedecision variable.

Accordingly, the optical signal power can be taken into account in thecalculation electronically.

According to another advantageous example, the receiving apparatusfurther comprises a second delay unit for providing the differentialphase shift between the previously received symbol and a symbol receivedbefore the previously received symbol to the calculation unit tocalculate the current value of the decision variable. Accordingly, aprevious differential phase shift can be taken into accountelectronically in the calculation improving the calculation result.

According to another advantageous example, the decision unit is adaptedto feed back a determined differential phase shift to the calculationunit. Accordingly, a previous differential phase shift can be taken intoaccount electronically in the calculation improving the calculationresult.

According to another advantageous example, the receiving apparatusfurther comprises an electro-optical arrangement for converting theoptical signal into the electrical signals comprising at least oneinterferometer. Accordingly, electrical signals may be obtained from anoptical signal.

According to another advantageous example, the electro-opticalarrangement comprises two phase controlled delay interferometers, andpreferably two balanced detectors may be connected to the twointerferometers so that one balanced detector is arranged at each delayinterferometer. Accordingly, an interference signal, such as a complexenvelope of a differentially decoded signal can be obtained.

According to another advantageous example, the electro-opticalarrangement comprises a free running two path interferometer coupled toa 3×3 optical coupler, and preferably three detectors are connected tothe 3×3 optical coupler so that one photo detector is arranged in seriesat each arm of the 3×3 optical coupler. Accordingly, the complexity ofthe electro-optical arrangement is reduced compared to two activelyphase-controlled delay interferometers, since only one interferometerwithout phase control can be used.

According to another advantageous example, the receiving apparatusfurther comprises an electronic phase converter for converting the threesignals output from the 3×3 coupler to two electrical signals to beinput in said input unit, and preferably the electro-optical arrangementis adapted to provide an electrical signal corresponding to the opticalsignal power to said input unit. Accordingly, three electrical signalsmay be provided to the input unit and subsequently to the calculationunit.

According to another embodiment, a receiving method for processing adifferential phase shift keying signal carrying a plurality of symbolscomprises receiving electrical signals derived from an optical signalafter self-homodyne reception; calculating a current value of a decisionvariable indicative of a differential phase shift in the optical signalbetween a currently received symbol and a previously received symbol asa function of at least one of the electrical signals representing theoptical signal power of the optical signal for the currently receivedsymbol and at least one previous value of the decision variable tocorrect for phase noise; and determining the differential phase shiftfrom the calculated current value of the decision variable to obtain thecurrently received symbol. Accordingly, the same additional performancegain achieved with the apparatus is similarly obtained by the aboveoperations that require, if at all, only minor modifications of theelectronic processing part, which is a processing device, and hence theadditional complexity is low. The method efficiently leads to obtainingthe current value of the decision variable and subsequently the currentsymbol quickly and accurately.

According to another embodiment, a computer program may be providedincluding instructions adapted to cause data processing means to carryout the method with the above features.

According to another embodiment, a computer readable medium may beprovided, in which a program is embodied, where the program is to make acomputer execute the method with the above features.

According to another embodiment, a computer program product may beprovided, comprising the computer readable medium.

Further advantageous features of the invention are described in theclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a receiving apparatus according to an embodiment ofthe invention.

FIG. 2 illustrates operations of a method for processing a differentialphase shift keying signal according to an embodiment of the invention.

FIG. 3 illustrates a fiber optic transmission system.

FIG. 4 illustrates a receiving apparatus with an electro-opticalarrangement and processing device in detail according to anotherembodiment of the invention.

FIG. 5 illustrates an example of an electro-optical arrangementaccording to an embodiment of the invention.

FIG. 6 illustrates another example of an electro-optical arrangementaccording to another embodiment of the invention.

FIG. 7 illustrates the performance improvement achieved with theembodiments of the invention.

FIG. 8 illustrates a simulation example of the performance improvementof the invention in comparison to other methods.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments of the invention are described with reference tothe figures. It is noted that the following description containsexamples only and should not be construed as limiting the invention.

Embodiments of the invention generally relate to processing adifferential phase shift keying signal carrying a plurality of symbols,and particularly, to calculate an improved value of a decision variableindicative of a differential phase shift by compensating for linear andnon-linear noise electronically so that a differential phase shift maybe obtained with high accuracy enabling to correctly decode the symbolrepresented by the differential phase shift.

In the following, an embodiment of the invention will be described withregard to FIG. 1.

FIG. 1 illustrates elements of a receiving apparatus 100 according to anembodiment of the invention, comprising a calculation apparatus 110 withan input unit 120 and a calculation unit 130 as well as a decision unit140.

The calculation apparatus 110 and the decision unit 140 are connected toexchange data. Further, the input unit 120 and the calculation unit 130in the calculation apparatus 110 are connected to exchange data thathave been input into the input unit 120.

The connections are preferably physical connections by fixed linesconnecting individual elements, however, these elements may also beplaced on a common circuit board and be wired appropriately.

The skilled person will appreciate that unit should not necessarily beunderstood as separate hardware elements but as a functional separation.

In a general case, the calculation apparatus 110 and the decision unit140 may be constituted by a processor with an appropriate interface,which is adapted to carry out the functions of the calculation unit 130and the decision unit 140 by software and/or hardware. Therefore, thefunctions might be changed or extended by software update or hardwareconfiguration. The functions performed in the receiving apparatus willbe described in detail later.

The calculation unit 130 and the decision unit 140 may be realized by amicroprocessor, computer, filed programmable gate array (FPGA) orintegrated circuit, such as an ASIC (application specific integratedcircuit) but are not limited thereto.

In detail, the receiving apparatus processes a differential phase shiftkeying signal carrying a plurality of symbols, i.e. different parts ofthe signal represent different symbols. Thereby, data transmission orsymbol transmission is realized on an optical carrier wave.

The input unit 120 receives electrical signals derived from an opticalsignal after self-homodyne reception. For example, the input unit 120can be an interface having a number of ports corresponding to the numberof electrical signals. It will be discussed below that the electricalsignals are derived from an optical signal, wherein the optical signalmay be transmitted as a phase modulated carrier wave through atransmission system.

The calculation unit 130 calculates a current value of a decisionvariable indicative of a differential phase shift in the optical signalbetween a currently received symbol and a previously received symbol asa function of at least one of the electrical signals representing theoptical signal power of the optical signal for the currently receivedsymbol and at least one previous value of the decision variable tocorrect for phase noise.

In detail, the calculation unit 130 receives the electrical signals fromthe input unit, in particular, electrical signals comprising anelectrical signal representing the optical signal power of the opticalsignal for the currently received symbol, and uses these electricalsignals for the calculation.

Further, a previous value of the decision variable is used for thecalculation, which may be the previously calculated value of thedecision variable, i.e. the value of the decision variable of one symbolperiod before, but it is also feasible to use a previously calculatedvalue of two symbol periods before, wherein the symbol period is thetime between two symbols, or two bits in BPSK. Using a previous value ofthe decision variable enhances the accuracy of the current value of thedecision variable, since the differential phase shift to be determinedis a phase shift between the currently received symbol and thepreviously received symbol. As will be discussed below, best results maybe achieved with multiple previous values of the decision variableconstituting a recursion relation averaging over previous values so thaterrors in individual values of previous decision variables aresuppressed.

The decision unit 140 then determines the differential phase shift fromthe current value of the decision variable obtained from the calculationunit 130 to obtain the currently received symbol. In detail, thedecision unit 140 uses the current value of the decision variable anddetermines depending on its value the differential phase shift, e.g. inDQPSK by plotting the complex value of the decision variable in thecomplex constellation diagram to obtain a point in the diagram. Theposition of this point in a quadrant of the constellation diagram isrelated to the phase difference between the currently received symboland the previously received symbol. This phase difference should thenroughly correspond to 0°, 90°, 180° or 270° in DQPSK, wherein the fourphase differences are then mapped to four symbols, e.g. “00”, “01”, “11”and “10”.

In the following operations of the receiving apparatus will be describedwith regard to FIG. 2. FIG. 2 illustrates a flow diagram of operationsof a method for processing a differential phase shift keying signalcarrying a plurality of symbols, such as during operation of thereceiving apparatus 100 shown in FIG. 1.

In a first operation 210, when starting operations, electrical signalsare received, which are derived from an optical signal afterself-homodyne reception. Electrical signals may comprise an electricalsignal corresponding to the optical signal power of the optical signalfor the currently received symbol and at least one of a real part of acomplex envelope of a differentially decoded signal and an imaginarypart of the complex envelope of a differentially decoded signal. How theelectrical signals are obtained exactly from the optical signal will bedescribed further below.

Then, in operation 220, the current value of the decision variableindicative of a differential phase shift in the optical signal between acurrently received symbol and a previously received symbol is calculatedas a function of at least one of the electrical signals representing theoptical signal power of the optical signal for the currently receivedsymbol and at least one previous value of the decision variable tocorrect for phase noise. The decision variable and the calculationthereof will be described in more detail further below.

In operation 230, the differential phase shift is determined from thecalculated current value of the decision variable to obtain thecurrently received symbol in the same way, as has been described abovewith respect to FIG. 1.

In the following, the application of the receiving apparatus 100 in afiber optic transmission system and the optical noise associated withsuch a system will be described with respect to FIG. 3, and afterwardsthe receiving apparatus 100 and the receiving method will be describedin more detail with respect to FIG. 4.

FIG. 3 illustrates a fiber-optic transmission system comprising atransmitter 300 and a receiver 310. Such a system may comprise severalhundred kilometers of fiber optics with amplifiers. The receiver 310 maybe regarded as the receiving apparatus 100. In between the transmitter300 and the receiving apparatus 310 M+1 amplifiers and M optical fiberspans may be provided. Each amplifier 320 amplifies the electric fieldof the optical wave but also generates amplified spontaneous emission(ASE) noise. This noise leads to linear phase noise and non-linear phasenoise in the fiber optic transmission system, due to refractive indexchanges in the transmission fiber 330 as well as in the other M-1transmission fibers.

FIG. 4 illustrates the receiving apparatus 400 comprising a processingdevice 410 and preferably an electro-optical arrangement 402 forreceiving an optical signal and converting it in electrical signals. Theprocessing device 410 comprises the previously discussed calculationapparatus 110 and decision unit 140 as well as two delay units 420 and430.

In detail, the block diagram depicted in FIG. 4 represents aself-homodyne receiving apparatus for differentially encoded opticalphase-modulated signals according to an embodiment of the presentinvention.

The skilled person will appreciate that both digital and analogueimplementations of the receiving apparatus 400 are possible.

The electro-optical arrangement 402 comprises a differential quadraturedetector 404 and a power detector 408 and yields the normalized opticalsignal power |y(n)|² and the complex envelope of the differentiallydecoded signalu(n)=y(n)y*(n−1)e ^(jπ/4)  (1),whose phase contains the received data. In equation (1), y(n) denotesthe normalized optical field for the currently received symbol andy*(n−1) denotes the complex conjugate of the normalized optical fieldfor the previously received symbol. The complex envelope may also becalled the phasor.

Here, a time discrete representation is used throughout for simplicityand without loss of generality, wherein n denotes the n-th symbolreceived at a time t=n·T. The skilled person will appreciate that thesame findings discussed herein, may also be applied to a continuousrepresentation with t and t+T.

Following the above referenced papers by Liu, the decision variablex(n)=y(n)z*(n−1)e ^(jπ/4)  (2)may be defined withz(n−1)=y(n−1)+wz(n−2)e ^(jΔφ(n−1))  (3)being an improved phase reference for the differential detectionprocess. The recursion relation effectively resembles a low passfiltering process and the skilled person will appreciate that otherfilter functions can be used for averaging the reference phase overprevious symbols. w is a weighting factor determining the strength ofthe filtering process. w=0 resembles standard self-homodyne receptionwithout averaging. The detected differential phase shiftΔφ(n−1)=φ(n−1)−φ(n−2 is obtained from the decision unit 140 andrenormalizes the reference signal to eliminate the influence of phasechanges resulting from the data modulation.

As shown in FIG. 4, the decision unit 140 may be adapted to feedback adetermined differential phase shift to the calculation apparatus 110 andcalculation unit 130. In detail, the decision unit 140 outputs thedifferential phase shift between the currently received symbol and thepreviously received symbol and a second delay unit 430 delays thesignal, e.g. by an interval T, and then provides the differential phaseshift between the previously received symbol and a symbol receivedbefore the previously received symbol, which is then input in thecalculation apparatus 110.

Substitution of equation (3) in (2 and some simply algebraicmanipulation employing equation (1) results in

$\begin{matrix}{{x(n)} = {{u(n)}{\left\{ {1 + {w\frac{x\left( {n - 1} \right)}{{{y\left( {n - 1} \right)}}^{2}}{\mathbb{e}}^{- {j{\lbrack{{{\Delta\phi}{({n - 1})}} + {\pi/4}}\rbrack}}}}} \right\}.}}} & (4)\end{matrix}$

Whilst equation (4) is in effect an infinite recursion relation, itshould be noted that the influence of higher order terms will decayrapidly for w≦1. Therefore, a value between 0 and 1 may be used andexperimentally, a value of 0.8 may be chosen so that the correction isweighted stronger for the last couple of symbols, e.g. roughly 10, thanfor symbols which have been received even a longer time ago.Particularly for digital realizations, a finite series representationwith a limited number of terms may be sufficient for practicalimplementations with adequate performance.

In equation (4) the term |y(n−1)|² denotes an optical signal power ofthe previously received symbol. This optical signal power is provided tothe calculation apparatus 110 and subsequently to the calculation unit130 through the input unit 120 by a first delay unit 420.

Both delay units 420 and 430 may be constituted by a register, memory orflip-flop to hold a certain value of the optical signal power, or to bemore concrete an electrical signal representing the optical signalpower, for a certain time to give out this value at a later time, inthis example after period T corresponding to the difference between twosymbols.

Therefore, the delay units 420 and 430 may provide values of the opticalsignal power and differential phase shift corresponding to a previouslyreceived symbol and thus previous values can be taken into account inthe calculation performed in the calculation unit 130.

On the other hand, non-linear phase noise leads to fluctuations of y(n)and consequently also fluctuations in the phasor u(n) which are notconsidered in equation (4).

In a multi-span optical transmission system, such as the fiber-optictransmission system shown in FIG. 3, the non-linear phase shift of y(n)due to the Kerr effect can be modelled by

$\begin{matrix}{{\phi_{nl}\left( \underset{.}{n} \right)} = {- {\sum\limits_{m = 1}^{M}{\gamma_{m}{{{y_{m}(n)} + {\sum\limits_{l = 1}^{m}{n_{{ASE},l}(n)}}}}^{2}{L_{{eff},m}.}}}}} & (5)\end{matrix}$

The index m denotes the m-th fiber span, γ_(m) and L_(eff,m) are thenon-linear coefficient and the effective non-linear length of the m-thfiber, respectively. y_(m) denotes the normalized optical field of thesignal at the input of the m-th fiber span and n_(ASE,m) the ASEcontribution of the m-th amplifier as discussed with respect to FIG. 3.

The effect of the non-linear phase shift is mitigated by reverting it atthe side of the receiving apparatus. As only the aggregate optical poweris observable at the receiving apparatus and not the individual signaland noise contributions at each span as contained in equation (5), thevariance of the non-linear phase noise is substantially reduced butcannot completely be eliminated.

In the following, non-linear phase noise compensation is integrated intoexecution of the above-discussed MSPE algorithm and independentadaptation factors are provided for both.

This is done by assuming a modified input signal for the normalizedoptical field{tilde over (y)}(n)=y(n)e ^(jκ|y(n)|) ²   (6)and repeating the calculation of equations (1)-(4), the equation

$\begin{matrix}{{x(n)} = {{u(n)}{\mathbb{e}}^{{j\kappa}{({{{y{(n)}}}^{2} - {{y{({n - 1})}}}^{2}})}}\left\{ {1 + {w\frac{x\left( {n - 1} \right)}{{{y\left( {n - 1} \right)}}^{2}}{\mathbb{e}}^{- {j{\lbrack{{{\Delta\phi}{({n - 1})}} + {\pi/4}}\rbrack}}}}} \right\}}} & (7)\end{matrix}$results, which describes a possible representation of the function to beimplemented in the calculation unit 130 of the calculation apparatus 110depicted in FIG. 4. It should be noted that this function is just onespecific example useful for correcting linear and non-linear noise andthe invention should not be construed to the specific representation ofthis function, since similar dependencies may be expressed in othersimilar ways leading to similar results.

Here, the exponential function e^(jκ|y(n)|) ² ^(−|y(n−1)|) ² ⁾ may beunderstood as follows. In contrast to random noise, deterministic noiseis proportional to the optical power. Therefore, using this exponentialfunction a possible phase error between the currently received symboland the previously received symbol may be compensated for by rotatingback the portion of the phase influenced by noise proportional to theoptical power, i.e. the optical power of the currently received symbolminus the optical power of the previously received symbol.

In equation (7) κ denotes an adaptation factor determining the strengthof the non-linear phase compensation, wherein κ=0 equals no non-linearphase compensation. In practice the adaptation factor κ and theweighting factor w are optimized adaptively, but an approximate valuefor κ may be derived as follows:

$\begin{matrix}{\kappa_{opt} \approx \frac{\sum\limits_{m = 1}^{M}{\gamma_{m}{Re}\left\{ {{y_{M + 1}(n)}{y_{m}^{*}(n)}} \right\}{\sum\limits_{k = 1}^{m}{\left\langle {{n_{{ASE},k}(n)}}^{2} \right\rangle L_{{eff},m}}}}}{{{y_{M + 1}(n)}}^{2}{\sum\limits_{m = 1}^{M + 1}\left\langle {{n_{{ASE},l}(n)}}^{2} \right\rangle}} \approx \frac{\sum\limits_{m = 1}^{M}{\gamma_{m}{\sum\limits_{k = 1}^{m}{\left\langle {{n_{{ASE},k}(n)}}^{2} \right\rangle L_{{eff},m}}}}}{\sum\limits_{m = 1}^{M + 1}\left\langle {{n_{{ASE},l}(n)}}^{2} \right\rangle} \approx {\gamma\; L_{eff}\frac{M}{2}}} & (8)\end{matrix}$

The parameters in equation (8) have been described above, and M+1denotes that the M+1 amplifier has been taken into consideration.

Several assumptions have been made when deriving equation (8). First, itis assumed that a high optical signal-to-noise ratio (OSNR) at thereceiving apparatus is present. The second approximation holds if thedispersion management is such that the signal shape is resembled at theoutput of each amplifier and the third approximation holds for identicalspans. In the simple case of identical spans and the non-linear phasenoise being the dominant impairment, it can be shown that NLPC reducesthe non-linear phase noise variance or increases the reach of thesystem.

In summary, the differential quadrature detector 404 provides thecalculation apparatus 110 with the complex envelope of thedifferentially decoded signal 411), e.g. in DQPSK its real part andimaginary part, and the power detector 408 provides the calculationapparatus 110 with the optical signal power for the currently receivedsymbol. This optical signal power may also be held in the second delayunit 420 to be provided to the calculation apparatus 110 at a later timeT so that the calculation apparatus 110 is provided with the opticalsignal power for the currently received symbol and the optical signalpower for the previously received symbol.

Similarly, the calculation apparatus is provided with the differentialphase shift ΔΦ(n) fed back to the first delay unit 430, where it isdelayed and then provided to the calculation apparatus 110 as thedifferential phase shift between the previously received symbol and asymbol received before the previously received symbol ΔΦ(n−1). Thedifferential phase shift is determined in the decision device 140 usingthe current value of the decision variable x(n) from the calculationapparatus 110, namely the real and imaginary part of the current valueof the decision variable in DQPSK. Finally, the calculation apparatus110 is provided with the weighting factor w and the adaptation factor κ,which have been described in detail above.

With the above-described inventive scheme only a moderate increase incomplexity in the electronic domain, i.e. of the processing device 410is necessary, wherein the complexity in the optical domain is notincreased.

In the following, the electro-optical arrangement 402 comprising thepower detector 408 and the differential quadrature detector 404 will bedescribed in more detail with respect to FIGS. 5 and 6.

The improved functionality and performance of the invenitve receivingapparatus can be obtained by using the electro-optical arrangement ofFIG. 5 or FIG. 6, for example.

FIG. 5 illustrates an electro-optical arrangement 500 according to anembodiment of the invention.

The electro-optical arrangement 500 may comprise a power splitter 510,two phase controlled Mach-Zehnder interferometers 522 and 524, twobalanced detectors 532 and 534, a detector 536 and three amplifiers 542,544, 546.

The power splitter 510, which may be a beam splitter, a 1×3 opticalcoupler or the like, splits the optical signal received by the receivingapparatus from an optical transmission system into three similar partsof the optical field. The detectors may be high-speed photodiodes.

The optical signal transmitted through the lowest arm in FIG. 5 issupplied to the detector 536 detecting the optical signal power andconverting it into an electrical signal, which may then preferably besupplied to the amplifier 546 that outputs an electrical signalcorresponding to the optical signal power. The detector 536 and theamplifier 546 in FIG. 5 constitute the power detector 408 of FIG. 4.

The two other arms coming from the power splitter 510 and carrying theoptical signal are each connected to the phase-controlled Mach-Zehnderinterferometer 522 and phase-controlled Mach-Zehnder interferometer 524,respectively. Each Mach-Zehnder interferometer 522, 524 has two arms orpaths and constitutes an optical delay interferometer with one arm beingdelayed by T, wherein T is the symbol period of the optical signal.

Further, an appropriate phase difference between the two interferometerarms is provided. The phase difference in the first Mach-Zehnderinterferometer 522 is set to −π/4 and the phase difference of the secondMach-Zehnder interferometer 524 is set to π/4.

In this arrangement, the two interferometers are differently affected byenvironmental influences, such as temperature, and thus phase controlshould be provided to maintain the phase difference between the twointerferometer arms and also between the two interferometers 522 and524.

The arrangement of the interferometers 522 and 524 with the delay T issuitable for self-homodyne reception, wherein the phase reference of alocal oscillator is replaced with the symbol received during theprevious period or interval. In DQPSK, the first interferometer 522 andthe second interferometer 524 correspond to an in-phase demodulator anda quadrature-demodulator.

In FIG. 5, two signals with different phase may each be obtained aftereach interferometer and the two optical signals of the firstinterferometer 522 having a difference in phase are detected by thebalanced detector 532, and the corresponding electrical signal may beamplified by the amplifier 542. This electrical signal may be consideredthe real part of the complex envelope of the differentially decodedsignal Re{u(n)} in DQPSK.

Similarly, the two optical signals of the interferometer 524 aredetected by the balanced detector 534 and the corresponding electricalsignal may be amplified by the amplifier 544 leading to an electricalsignal, which may be considered the imaginary part of the complexenvelope of the differentially decoded signal Im{u(n)} in DQPSK.

Therefore, the two interferometers 542 and 524, the balanced detectors532 and 534 as well as the amplifiers 542 and 544 constitute thedifferential quadrature detector 404 of FIG. 4.

In this arrangement two balanced detectors and two amplifiers areconnected to the two phase-controlled delay interferometers so that onebalanced detector and one amplifier is arranged in series at each delayinterferometer. However, the skilled person will appreciate that asimilar arrangement, for example with a different number of amplifiersor different detectors, may lead to the same results. Optionally, theamplifiers may be preamplifiers or may be omitted altogether, forexample.

With the electro-optical arrangement, the optical signal received at thepower splitter 510 is converted into electrical signals, namely in thiscase three electrical signals corresponding to the real and imaginarypart of the complex envelope of the differentially decoded signal and anelectrical signal corresponding to the optical signal power. The delaysand transfer functions/bandwidth of the three different electronic pathsneed to be matched for optimum performance.

These electrical signals are then provided to the processing device 410,which can be analog or digital and has been described in detail in FIG.4. In the digital case, clock recovery, A/D-conversion and sampling maybe applied at the output of the electro-optical arrangement 500.

Next, another embodiment of the invention illustrating anotherelectro-optical arrangement 600 is described with respect FIG. 6. Thiselectro-optical arrangement 600 may also be used together with theprocessing device 410 of FIG. 4 forming together the receivingapparatus.

The electro-optical arrangement 600 comprise, for example, a powersplitter 610, a Mach-Zehnder interferometer 620, a 3×3 coupler 625, fourdetectors 632, 634, 636, 638, four amplifiers 642, 644, 646, 648, and anelectronic phase converter 650.

In this embodiment described in FIG. 6, the electro-optical arrangement600 comprises only one Mach-Zehnder interferometer which is preferably afree running two path interferometer coupled to a 3×3 optical coupler625 and has a delay equal to the bit period or symbol period, if asymbol contains more than one bit, which is the case in DQPSK.

Therefore, the interferometer does not need any active optical phasecontrol, thereby eliminating any optical control required at thereceiving side. This may be understood by considering that each signalof the three arms coming from the interferometer and the 3×3 coupler isshifted by 2π/3 with respect to each other so that no information islost, and if required, the phase may be rotated back electronically at alater stage for each of the three signals the same way.

Here, the power splitter 610 may be the same component as in FIG. 5,however, in this case only splitting the optical signal in two parts,wherein one part of the optical signal is transmitted through the lowestarm in FIG. 6 and is detected by the detector 638, which may be aphotodiode, and is preferably amplified by the amplifier yielding anelectrical signal corresponding to the optical signal power |y(n)|².

The other part of the optical signal is input into the Mach-Zehnderinterferometer 620, which has been described above and does not requirephase control. Similarly to the phase controlled Mach-Zehnderinterferometers of FIG. 5, the delay interval of T in one of the arms ofthe interferometer 620 is suitable for self-homodyne reception.

The output of the interferometer 620 of FIG. 6 yields a three phasesignal

$\begin{matrix}{\begin{bmatrix}{a(n)} \\{b(n)} \\{c(n)}\end{bmatrix} = {\frac{1}{6}\left\{ {{{y(n)}}^{2} + {{y\left( {n - 1} \right)}^{2}} + \begin{bmatrix}{2{Re}\left\{ {{y(n)}{y^{*}\left( {n - 1} \right)}{\mathbb{e}}^{{j\phi}_{err}}} \right\}} \\{2{Re}\left\{ {{y(n)}{y^{*}\left( {n - 1} \right)}{\mathbb{e}}^{j{({\phi_{err} - {2{\pi/3}}})}}} \right\}} \\{2{Re}\left\{ {{y(n)}{y^{*}\left( {n - 1} \right)}{\mathbb{e}}^{j{({\phi_{err} + {2{\pi/3}}})}}} \right\}}\end{bmatrix}} \right\}}} & (9)\end{matrix}$which is detected by the three detectors 632, 634 and 636.

The detectors in the electro-optical arrangement 600 may be photodiodes,high-speed photodiodes, or more specifically single ended photodiodeshaving optionally electronic preamplifiers. A phase shift of theinterferometer translates into the same fading of the phase in theelectronic domain so that phase control may be performed electronicallyat a later stage as discussed above.

Assuming that this fading effect is compensated for by a feed-forward ora closed loop phase control in the electronic domain, the previoustwo-phase signal of equation (1) can be obtained asu(n)=(2a−b−c)+j√{square root over (3)}(b−c)  (10).

It should be noted that the 3×3 coupler 625 does not need to besymmetric for generation of the three phase signal and the subsequentconversion into a two phase signal, wherein the two phase signalcorresponds to the signal obtained with the electro-optical arrangement500 of FIG. 5 after conversion by the electronic phase converter 650 ofthe three signals output from the 3×3 coupler to two electrical signalto be input in the input unit 120 of the processing device 410.

In FIG. 6, three detectors 632, 634 and 636, and three amplifiers arepreferably connected to the 3×3 optical coupler 625 so that onephotodetector and one amplifier is arranged in series at each arm of the3×3 optical coupler 625. This constitutes a simple and cheap arrangementfor converting the three parts of the optical signal in electricalsignals. However, it should be understood that the invention is notlimited to this arrangement and a different amount of amplifiers may beused.

The electrical signal corresponding to the optical signal power |y(n)|²obtained from the detector 638 and the real and imaginary parts of thecomplex envelope of the differentially decoded signal obtained from theelectronic phase converter 650 are output from the electro-opticalarrangement 600 to the input unit 120, similar to the electrical signalsof the processing device 410 of FIG. 4.

However, note that the electro-optical arrangement 600 of FIG. 6 needsto provide only four detectors and not five as in FIG. 5, since balanceddetectors are not needed and only one free-running interferometerinstead of two phase-controlled interferometers is used. Also, comparedto a standard self-homodyne DUSK receiver, the electro opticalarrangement of FIG. 6 needs only one free-running interferometer insteadof two stabilized interferometers.

FIG. 7 illustrates the performance improvement in the linear regime andthe non-linear regime. The launch power of the optical signal is plottedon the x-axis in the diagram of FIG. 7 and the Q-factor is plotted onthe y-axis. The performance improvement in the linear regime is mainlythrough the MSPE scheme whereas in the non-linear regime MSPE and NLPCschemes determine the overall performance improvement together.

Finally, FIG. 8 illustrates the effectiveness of the invention in asimulation of a simple configuration. A 43 Gb/s RZ-DQPSK signal, RZ(return to zero) determining the pulse form, is transmitted over 80 kmof a standard single mode fiber (SSMF, with dispersion D=17 ps/nm/km,attenuation α=0.21 dB/km, γ=1.37/W/km, residual dispersion Dres=0ps/nm). The optical signal to noise ratio (OSNR) is equal to the launchpower (P_(launch))+2 dB and plotted on the x-axis and the Q-factor isplotted on the y-axis. The SSMF is fully dispersion compensated by adispersion compensating fiber (DCF). The launch power and the receivedoptical signal to noise ratio (OSNR, referenced to an optical bandwidthof 0.1 nm) are varied between 10 . . . 18 dBm and 12 . . . 20 dB,respectively. High power levels are chosen to obtain a level ofnon-linear phase noise similar to that generated over a large number offiber spans. The influence of the optical receive amplifier isneglected. For comparison also a simulation without any compensationscheme (uncomp) is shown in FIG. 8.

The system performance is simulated and assessed by means of thesystem's Q-factor (a Q of 10 dB equals a bit error ratio of 7.8e−3).Without the transmission link, OSNR=12 dB is required for Q=9.5 dB. TheNLPC scheme alone does not yield a significant performance improvementin the linear regime, whereas the performance gain through theMSPE/MSPE-E scheme is reduced in the non-linear regime. The inventivescheme provides best overall performance. It yields a performanceimprovement of approximately 0.3 dB over the MSPE/MSPE-E scheme in thepeak region and a performance improvement of approximately 0.8 dB overthe MSPE/MSPE-E/NLPC scheme in the non-linear regime.

In summary, the invention provides an improved transmission performancein the non-linear regime over MSPE and MSPE-E by suitable integration ofNLPC into the MSPE-E scheme yielding the described inventive scheme andan improved transmission performance in the linear regime overelectronic NLPC implementation.

Although most examples above relate to DQPSK, the invention is notlimited to DQPSK and may be applied to all schemes involving adifferential phase shift or schemes in which a differential phase shiftis mixed with other modulation schemes, such as amplitude shift keying(ASK). For example, quadrature amplitude modulation (QAM), andespecially 16-QAM, may benefit from the invention.

According to another embodiment a program may be provided includinginstructions adapted to cause a data processor that may be included inthe processing device 410 or calculation apparatus 110 to carry outcombinations of the above-described operations.

The program or elements thereof may be stored in a memory, such as ROMor RAM or other suitable storage device of the processing device 410,and retrieved by the processor for execution.

Moreover, a computer readable medium may be provided, in which theprogram is embodied. The computer readable medium may be tangible suchas a disk or other data carrier or may be constituted by signalssuitable for electronic, optic or any other type of transmission. Acomputer program product may comprise the computer readable medium.

It should be understood that the operations described herein are notinherently related to any particular device or apparatus and may beimplemented by any suitable combination of components. The apparatuses,devices and units described in detail above constitute preferredembodiments to perform the operations of the described methods. However,this may not be limited to the same.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the apparatuses and devicesand methods of the invention as well as in the construction of thisinvention without departing from the scope of or spirit of theinvention.

The invention has been described in relation to particular exampleswhich are intended in all respects to be illustrative rather thanrestrictive. Those skilled in the art will appreciate that manydifferent combinations of hardware, software and firmware will besuitable for practicing the present invention.

Moreover, other implementations of the invention will be apparent tothose skilled in the art from consideration of the specification andpractice of the invention disclosed herein. It is intended that thespecification and the examples be considered as exemplary only. To thisend, it is to be understood that inventive aspects lie in less then allfeatures of a single foregoing disclosed implementation orconfiguration. Thus, the true scope and spirit of the invention isindicated by the following claims.

The invention claimed is:
 1. A receiving apparatus for processing adifferential phase shift keying signal carrying a plurality of symbols,comprising an input unit for receiving electrical signals Re(u(n),Im(u(n), |y(n)|² derived from an optical signal after self-homodynereception; a calculation unit for calculating a current value of adecision variable x(n) indicative of a differential phase shift in theoptical signal between a currently received symbol and a previouslyreceived symbol as a function of at least one of the electrical signalsrepresenting the optical signal power of the optical signal for thecurrently received symbol |y(n)|² and at least one previous value of thedecision variable x(n−1), x(n−2) to correct for phase noise; a decisionunit for determining the differential phase shift from the current valueof the decision variable x(n) obtained from the calculation unit toobtain the currently received symbol; an electro-optical arrangement forconverting the optical signal into the electrical signals comprising atleast one interferometer, wherein the at least one interferometer is afree running two-path interferometer coupled to a 3×3 optical coupler;and an electronic phase converter for converting three signals outputfrom the 3×3 coupler two electrical signals to be input in said inputunit.
 2. The receiving apparatus of claim 1, wherein the calculationunit is configured to base the calculation of the decision variable onat least one of a difference between optical signal powers of theoptical signal for the currently received symbol and for a previouslyreceived symbol |y(n)|²−|y(n−1)|², an optical signal power of thepreviously received symbol |y(n−1)|²), a weighting factor w, anadaptation factor κ determining the strength of nonlinear phasecompensation, a symbol period of the optical signal T, and adifferential phase shift between the previously received symbol and asymbol received before the previously received symbol Δφ(n−1).
 3. Thereceiving apparatus of claim 2, wherein the calculation unit isconfigured to calculate the current value of decision variable using amultiplication factor representable ase ^(jκ(|y(n)|) ² ^(−|y(n−1)|) ² ⁾ wherein κ denotes the adaptationfactor and |y(n)|²−|y(n−1)|² denotes the difference between the opticalsignal powers of the optical signal for the currently received symboland for the previously received symbol.
 4. The receiving apparatus ofclaim 2, wherein the calculation unit is configured to perform thecalculation of the current value of decision variable x(n) on a basis ofan equation representable as:${x(n)} = {{u(n)}{\mathbb{e}}^{{j\kappa}{({{{y{(n)}}}^{2} - {{y{({n - 1})}}}^{2}})}}\left\{ {1 + {w\frac{x\left( {n - 1} \right)}{{{y\left( {n - 1} \right)}}^{2}}{\mathbb{e}}^{- {j{\lbrack{{{\Delta\phi}{({n - 1})}} + {\pi/4}}\rbrack}}}}} \right\}}$wherein u(n) denotes a complex envelope of the differentially decodedsignal, κ denotes the adaptation factor, |y(n)|²−|y(n−1)|² denotes thedifference between the optical signal powers of the optical signal forthe currently received symbol and for the previously received symbol, wdenotes the weighting factor, x(n−1) denotes the previous value of thedecision variable, |y(n−1)|² denotes the optical signal power of thepreviously received symbol and Δφ(n−1) denotes the differential phaseshift between the previously received symbol and a symbol receivedbefore the previously received symbol.
 5. The receiving apparatus ofclaim 1, wherein the electrical signals correspond to the optical signalpower of the optical signal for the currently received symbol |y(n)|²and at least one of the real part of the complex envelope of thedifferentially decoded signal Re(u(n) and the imaginary part of thecomplex envelope of the differentially decoded signal Im(u(n).
 6. Thereceiving apparatus of claim 1, further comprising a first delay unitfor providing the electrical signal corresponding to the optical signalpower of the previously received symbol |y(n−1)|² to the calculationunit to calculate the current value of the decision variable x(n). 7.The receiving apparatus of claim 6, further comprising a second delayunit for providing the differential phase shift between the previouslyreceived symbol and a symbol received before the previously receivedsymbol Δφ(n−1) to the calculation unit to calculate the current value ofthe decision variable x(n).
 8. The receiving apparatus of claim 1,wherein the decision unit is adapted to feed back a determineddifferential phase shift to the calculation unit.
 9. The receivingapparatus of claim 1, further comprising three photo detectors connectedto the 3×3 optical coupler so that one detector is arranged at each armof the 3×3 optical coupler.
 10. The receiving apparatus of claim 1,wherein the electro-optical arrangement is adapted to provide anelectrical signal corresponding to the optical signal power to saidinput unit.
 11. A receiving method for processing a differential phaseshift keying signal carrying a plurality of symbols, comprising:receiving electrical signals Re(u(n), Im(u(n), |y(n)|² derived from anoptical signal after self-homodyne reception; calculating a currentvalue of a decision variable x(n) indicative of a differential phaseshift in the optical signal between a currently received symbol and apreviously received symbol as a function of at least one of theelectrical signals representing the optical signal power of the opticalsignal for the currently received symbol |y(n)|² and at least oneprevious value of the decision variable x(n−1), x(n−2) to correct forphase noise; determining the differential phase shift from thecalculated current value of the decision variable x(n) to obtain thecurrently received symbol; converting the optical signal into theelectrical signals, and converting three signals output from a 3×3coupler to two electrical signals to be input in an input unit.